Этот пакет весит пятьсот граммов.

Because пакет is a masculine singular noun. In Russian, words like this must agree with the noun in gender, number, and case.

So:

• этот пакет = this package / this bag (masculine)
• эта сумка = this bag (feminine)
• это окно = this window (neuter)
• эти пакеты = these packages (plural)

Here, пакет is masculine, so этот is the correct form.

Весит is the 3rd person singular present tense form of весить, meaning to weigh.

So:

• я вешу = I weigh
• ты весишь = you weigh
• он / она / оно весит = he / she / it weighs
• они весят = they weigh

In this sentence, the subject is этот пакет (this package), which is singular, so Russian uses весит: this package weighs.

No. These are different verbs, and learners often confuse them because they look similar.

• весить = to weigh
• висеть = to hang / to be hanging
• вешать = to hang something up

Examples:

• Пакет весит пятьсот граммов. = The package weighs 500 grams.
• Картина висит на стене. = The picture is hanging on the wall.
• Я вешаю куртку. = I am hanging up the jacket.

So in your sentence, весит definitely means weighs, not hangs.

Because 500 is written in Russian as the single word пятьсот.

It is made historically from пять (five) + сто (hundred), but in modern Russian it is treated as one numeral word.

A few examples:

• двести = 200
• триста = 300
• четыреста = 400
• пятьсот = 500

This word also changes form when declined, for example:

• пятьсот граммов = 500 grams
• без пятисот граммов = without 500 grams
• к пятистам граммам = toward 500 grams

But in your sentence, пятьсот is the normal dictionary form.

Because after numerals like 5 and higher, Russian normally uses the genitive plural form of the noun.

So:

• 1 грамм
• 2, 3, 4 грамма
• 5, 6, 7 ... граммов

Since пятьсот is 500, the standard form is:

пятьсот граммов

This is a very important Russian number pattern:

• один килограмм
• два килограмма
• пять килограммов

You may also hear грамм instead of граммов, especially in everyday speech and especially with units of measure. But пятьсот граммов is the careful standard form.

This is a slightly advanced question, but a good one.

After весить in the sense of to weigh, the amount is usually treated as a measure expression functioning like a direct object. In practice, you get the normal numeral pattern:

• the numeral appears in the form required by the sentence
• the counted noun follows the numeral rules

Here, the phrase is:

пятьсот граммов

The noun граммов is in the genitive plural because it follows пятьсот.

As for пятьсот, its nominative and accusative forms are the same, so you do not see a difference here.

So the short practical answer is: learn the whole chunk весить + number + unit, for example:

• весить килограмм
• весить три килограмма
• весить пять килограммов

Because Russian does not need one here.

In English, the sentence is This package weighs 500 grams. The main verb is weighs, not is. Russian works the same way: the verb весит already carries the meaning.

So:

• Этот пакет весит пятьсот граммов. = This package weighs 500 grams.

There is no missing is.

Learners sometimes ask this because Russian often omits present-tense to be in sentences like:

• Это пакет. = This is a package.

But your sentence is different, because it already has a real verb: весит.

Yes, Russian word order is flexible, but the neutral order here is:

Этот пакет весит пятьсот граммов.

That sounds natural and straightforward.

Other orders are possible for emphasis, for example:

• Пятьсот граммов весит этот пакет.
  This emphasizes the weight.

• Этот пакет пятьсот граммов весит.
  This is possible in speech, often with a particular rhythm or emphasis.

So yes, word order can change, but the original sentence is the safest default for learners.

Yes, if the context already makes it clear which package you mean.

• Пакет весит пятьсот граммов. = The package weighs 500 grams. / A package weighs 500 grams.

Adding этот makes it specifically this package.

Compare:

• этот пакет = this package
• тот пакет = that package

So этот is not required for grammar, but it adds deixis: it points to a specific nearby or currently relevant item.

The stress is:

Э́тот паке́т ве́сит пятьсо́т гра́ммов.

A rough English-style guide could be:

EH-tət pa-KYET VYE-sit pyat-SOT GRAM-əf

A few useful pronunciation notes:

• Russian unstressed о often sounds closer to a.
• Final в in граммов is pronounced like f.
• пятьсот has the stress on the second part: -сот.

If you want to sound natural, the rhythm is usually fairly even:

Э́тот паке́т | ве́сит | пятьсо́т гра́ммов.